Rational category and cone length of Poincare complexes

We prove the so-called Lemaire-Sigrist conjecture for 1-connected Poincare: complexes, namely that for such spaces rational Lusternik-Schnirelmann category equals rational cone length. We also prove that the attachment of the top cell in such a space raises rational L-S category by one. (C) 1998 Elsevier Science Ltd. All rights reserved.